Radar would be quite a lot of RF radiation!
That said, sinking say 10W of heat into your organs overnight is going to do serious damage.
Is it? Electric heating pads and electric blankets are certainly a thing, and they're around 10W (the one I have says 50W).
I made the mistake of trying to see if I could feel the 5 watts of RF energy coming from the radio side of the plate. I stuck the panel to my palm, keyed the mic, and instantly felt a searing, stabbing pain in my hand. It felt like a hot nail was jammed into the meat of my palm and was very surprisingly painful.
As blattimwind said above, the distribution of RF energy in the body is going to be very unpredictable at that distance and you could have hot spots deep in the tissue that are not innervated. If you got a hot spot anywhere near what I experienced with that CB antenna I'm absolutely confident there would be tissue damage.